6th
Subject/Grade or Course:
Math
Major (m) Common Core cluster for the
Unit:
 6.RP Understand ratio concepts and use
ratio reasoning to solve problems.
 6.NS Compute fluently with multi-digit
numbers and find common factors and
multiples.
SAXON LINK
Lesson 10 Saxon course 2
Investigation I Saxon Course 2
Lesson 15, 16 Saxon Course 2
Lesson 36 Saxon Course 2
Lesson 46, 48, 50 Saxon Course 2
Common Core Cluster # from above:
 6.RP
 6.NS
SAXON LINK
Lessons 1-10 Saxon Course 2
Lesson 10 Saxon course 2
Investigation I Saxon Course 2
Lesson 15, 16 Saxon Course 2
1
MATHEMATICS
Unit Name: Ratios and Proportions
Supporting and Additional (s/a) Common
Core Standards for the Unit:
 6.RP.1. Understand the concept of ratio
and use ratio language to describe a ratio
relationship between two quantities.
 6.RP.2. Understand the concept of a unit
rate a/b associated with a ratio a:b with b ≠
0, and use rate language in the context of a
ratio relationship.
 6.RP.3a-d. Use ratio and rate reasoning to
solve real-world and mathematical
problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double
number line diagrams, or equations.
 6.NS.4. Find the greatest common factor
of two whole numbers less than or equal to
100 and the least common multiple of two
whole numbers less than or equal to 12.
Common Core Supporting / Additional
(s/a) Standards # from above:
 6.RP.1
 6.RP.2
 6.RP.3a-d
 6.NS.4
Pacing: 6 weeks
Bridging Common Core Standards from
Previous Grade(s):
 5.NF Use equivalent fractions as a strategy
to add and subtract fractions.
 5.NF Apply and extend previous
understandings of multiplication and
division to multiply and divide fractions.
 5.G Graph points on the coordinate plane
to solve real world and mathematical
problems.
Common Core Bridging Standards from
Previous Grade(s)# from above:
 5.NF.1
 5.NF.2
 5.NF.1
 5.NF.2a-b
 5.NF.3a-b
 5.NF.4
 5.NF.5a-c
 5.G.1
 5.G.2
MATHEMATICS
Subject/Grade or Course:
Math
Unit Name: Ratios and Proportions
Pacing: 6 weeks
Structure of Math / Overarching Understanding(s):
Essential Questions:
 Use reasoning with ratios and rates to solve real-world and
 How can reasoning with ratios and rates help solve real-world
mathematical problems.
and mathematical problems?
Teacher Note:
 How are ratios and percents alike? How are they different?
o Relationships between fractions, decimals, and percents are
 How do you determine a unit rate given a table of values?
developed in this unit. Students learn how these forms are
 What are the differences between converting measurements in
related to one another and make decisions about when to use
the metric and standard measurement systems?
each form.
 Given the quantity and price of two objects, how can you
o Understanding and applying the relationships between
determine which one is the better buy?
fractions, decimals, and percents, students will solve real How are fractions, decimals, and percents related?
world problems such as unit rate, measurement conversions,
 How are common factors and multiples applied to solve realconstant rate, and comparison of quantities.
world scenarios?
o Fractions are viewed as rates, ratios, or parts of a proportion
 How can I use multiplication and division to solve ratio and
to provide underpinnings needed in seventh grade for work
rate problems?
with proportional reasoning.
 What is the difference between a ratio and a rate?
 How can I use tables of equivalent ratios, tape diagrams,
double number line diagrams, or equations to compare rates of
change?
STUDENT-FRIENDLY LEARNING TARGET STATEMENTS
MP.2 Reason abstractly and quantitatively.
Learning Targets
6.RP.1 Understand
MP.4 Model with mathematics.
the concept of ratio
MP.6 Attend to precision.
and use ratio
MP.7 Look for and make use of structure.
language to describe
 Compare and contrast the properties of ratios and fractions.
a ratio relationship
o I understand that ratios compare part to part and fractions do not.
between two
 Create a variety of models to show ratios in real-world settings.
quantities.
o I can model real world ratios using appropriate symbols.
 Create examples of ratios and explain their meaning.
o I can create examples of ratios in context.
SAXON LINK:
o I can explain the meaning and context of any ratio.
SAXON Course 2
 Apply the use of ratios to real-world situations.
Section 1
o I can translate a ratio into a real world problem.
 Use ratio language to describe a comparison of two quantities which can be written as a to b, a/b, or a:b.
6th
2
MATHEMATICS
Subject/Grade or Course:
Math
Unit Name: Ratios and Proportions
o I can describe ratios and their symbols using correct vocabulary.
o I can select the correct symbols to express ratios three ways.
o I can compare two quantities using a ratio.
6th
6.RP.2 Understand
the concept of a unit
rate a/b associated
with a ratio a:b with
b ≠ 0, and use rate
language in the
context of a ratio
relationship.
SAXON LINK:
Saxon 8/7 and
course 2
Section 1
3
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
 Create unit rates to name the amount of either quantity, in terms of the other quantity.
o I can write a unit rate.
o I can describe the relationship between the two quantities in a unit rate.
 Demonstrate understanding of unit rate.
o I can illustrate a unit rate using multiple models.
o I can explain unit rates using appropriate vocabulary.
 Interpret the relationship between unit rates and ratios.
o I understand that all ratios can be expressed as unit rates.
o I can model the relationship between the unit rate and a ratio.
 Generate ratios for a variety of unit rates.
o I can increase and decrease unit rates to provide solutions for real-world situations.
Pacing: 6 weeks
MATHEMATICS
Subject/Grade or Course:
Math
Unit Name: Ratios and Proportions
Pacing: 6 weeks
6.RP.3.a Make tables MP.1 Make sense of problems and persevere in solving them.
of equivalent ratios
MP.2 Reason abstractly and quantitatively.
relating quantities
MP.3 Construct viable arguments and critique the reasoning of others.
with whole number
MP.4 Model with mathematics.
measurements, find
MP.5 Use appropriate tools strategically.
missing values in the MP.6 Attend to precision.
tables, and plot the
MP.7 Look for and make use of structure.
pairs of values on the  Create table of equivalent ratios using real-world examples.
coordinate plane. Use
o I understand that all ratios in a ratio table are equivalent.
tables to compare
o I understand that every ratio has an infinite number of equivalent ratios.
ratios
o I can create a ratio table using real-world examples.
SAXON LINK:
 Find missing values within a ratio table.
Saxon 7/6
o I can apply previous ratio knowledge to find missing values in a table.
L 105
 Compare ratios using tables.
L 41
o I can expand ratio tables to compare ratios.
L 43
o I can describe the multiplicative value of ratios.
 Plot pairs of values from a ratio table on a coordinate plane.
o I can plot pairs on a coordinate plane from a ratio table.
6.RP.3.b Solve unit
MP.1 Make sense of problems and persevere in solving them.
rate problems
MP.2 Reason abstractly and quantitatively.
including those
MP.3 Construct viable arguments and critique the reasoning of others.
involving unit
MP.4 Model with mathematics.
pricing and constant
MP.5 Use appropriate tools strategically.
speed. For example,
MP.6 Attend to precision.
if it took 7 hours to
MP.7 Look for and make use of structure.
mow 4 lawns, then at MP.8 Look for and express regularity in repeated reasoning.
that rate, how many
 Construct and reason about real-world problems involving unit pricing and constant speed.
lawns could be
o I can construct models to solve real-world problems involving unit price and constant speed.
mowed in 35 hours?
o I can evaluate and determine accuracy of a solution.
At what rate were
o I can provide evidence to defend my solution.
lawns being mowed?  Solve unit rate problems involving unit pricing.
o I can transfer my unit rate knowledge to solve problems containing unit price.
SAXON LINK:
 Solve unit rate problems involving constant speed.
Investigation 1
6th
4
MATHEMATICS
Subject/Grade or Course:
Math
Unit Name: Ratios and Proportions
o I can calculate constant speed using unit rates.
Saxon 8/7
6th
6.RP.3.c Find a
percent of a quantity
as a rate per 100
(e.g., 30% of a
quantity means
30/100 times the
quantity); solve
problems involving
finding the whole,
given a part and the
percent.
SAXON LINK
SAXON 8/7
LESSON 15
LESSON 36
SAXON 7/6
Lesson 105
5
Pacing: 6 weeks
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
 Construct models of equivalent fractions, decimals, and percents.
o I can model equivalent fractions, decimals, and percents.
 Convert decimals to percentages.
o I can provide the equivalent percentage given a decimal.
 Convert fractions to percentages.
o I can provide the equivalent percentage given a fraction.
 Explain the relationship between fractions, decimals, and percents.
o I can create and justify a conjecture explaining the relationship between fractions, decimals, and percents.
 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 or 0.3 times the quantity).
o I can construct a model showing a percent using ratio concepts.
 Given a part and the percent, solve problems to find the whole.
MATHEMATICS
Subject/Grade or Course:
Math
Unit Name: Ratios and Proportions
o I can use equivalent ratio knowledge to find the whole given the percent and the part.
6th
6.RP.3.d Use ratio
reasoning to convert
measurement units;
manipulate and
transform units
appropriately when
multiplying or
dividing quantities.
SAXON LINK
SAXON 8/7
LESSON 15
LESSON 36
Lessons 81-85
6
Pacing: 6 weeks
MATHEMATICAL PRACTICES
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
 Create a model to demonstrate equivalent units of measure.
o I can construct a variety of models showing equivalency within measurement units.
 Use models to discover the mathematical operation to extend the pattern.
o I can extend patterns using a model.
o I can examine and analyze a pattern to determine the mathematical operation used.
 Explain a comparison between various equivalent units of measure as a ratio (12 inches = 1 foot, 12:1).
o I can describe the relationship between equivalent units of measure and ratios.
MATHEMATICS
Subject/Grade or Course:
Math
Unit Name: Ratios and Proportions
Pacing: 6 weeks
6.NS.4. Find the
MP.1 Make sense of problems and persevere in solving them.
greatest common
MP.2 Reason abstractly and quantitatively.
factor of two whole
MP.3 Construct viable arguments and critique the reasoning of others.
numbers less than or MP.5 Use appropriate tools strategically.
equal to 100 and the
MP.6 Attend to precision.
least common
MP.7 Look for and make use of structure.
multiple of two
MP.8 Look for and express regularity in repeated reasoning.
whole numbers less
 Distinguish prime from composite numbers.
than or equal to 12.
o I can classify prime and composite numbers.
 Apply divisibility rules.
SAXON LINK:
o I can make and defend a conjecture involving divisibility rules.
Saxon 8/7
o I can apply divisibility rules.
Lesson 6, 21. 27
 Decompose (break down) numbers into factors.
o I can use divisibility rules to decompose numbers into factors.
Saxon 7/6
o I can represent a number as the product of its factors.
L 19, 20, 30
o I can find the prime factorization of a number using various models.
 Demonstrate the use of prime factorization to find common factors and multiples.
o I can apply the concept of prime factorization to find common factors and multiples.
 Find the greatest common factor of two whole numbers less than or equal to 100.
o I can apply various strategies to find the greatest common factor of two whole numbers.
 Find the least common multiple of two whole numbers less than or equal to 12.
o I can apply various strategies to find the least common multiple of two whole numbers.
 Apply the distributive property to express any sum as a multiple of a GCF and the sum of two whole numbers.
o I understand and can use the distributive property.
o I can identify the greatest common factor using the distributive property.
Assessment Tasks  Claim #1/DOK 1, 2, 3, 4 (circle one):
that Provide
 Claim #2/DOK 1, 2, 3, 4 (circle one):
Evidence for Claims  Claim #3/DOK 1, 2, 3, 4 (circle one):
including DOK
 Claim #4/DOK 1, 2, 3, 4 (circle one):
6th
Materials/Resources http://commoncoretools.files.wordpress.com/2012/02/ccss_progression_rp_67_2011_11_12_corrected.pdf
http://schools.nyc.gov/NR/rdonlyres/A9F735CB-47E4-40F8-884FEA54D0AB5705/0/NYCDOEG6MathRatios_Final.pdf
7
MATHEMATICS
Subject/Grade or Course:
Math
Unit Name: Ratios and Proportions
Pacing: 6 weeks
http://illustrativemathematics.org/standards/k8
Developing Essential Understanding of Ratios, Proportions & Proportional Reasoning Grades 6-8 NCTM
6th
Teacher Notes
8
We did not have time to add assessment tasks within the claims. Please see the above resources for excellent
examples.